Analog summing emulation idea

[Kingston]

Taking an computer generated 1 kHz @ 44.1 kHz sample rate will make it impossoble to delay 10 µs without interpolation (as the smallest possible delay @ 44.1 kHz is 1/44100 ~= 25 µs).

Maybe I missed the point completly, but I see no direct relation to nyquist here... of course, nyquist is extremly important when dealing with AD/DA, but wasn't at all the topic I was talking about

You are right, in a sense. 44.1khz can't do it without an allpass filter (oversampled), but this is where nyquist theory (and discrete digital signal representation) has a very significant importance. It is DIRECTLY related to the issue, and if you studied it a bit more you'd find out why.

Similarly, no examples with mic placement (even when moved a millimeter), and perception of direction do not work here. It's simply the way nyquist works. 44.1khz DOES capture even the smallest changes in mic placement.

It's not the easiest of things to grasp, and there's no easy way of doing the "nyquist 101", unfortunately.

It's not just a simple issue of nudging 1 sample either way. It's the complex interaction of time vs. amplitude vs. the resulting nyquist sine formula (basically sinc) that deal with both frequency and phase.

'Any bandlimited sine wave can be represented by drawing only two points in discrete time' (yes, that's only two samples needed for one perfect sine wave)

Understand that, you're a good way off of the placebo land.

[Aleksey Vaneev]

friteuse, now I do not understand how that relates to 100kHz frequencies... You were talking about phase difference perception - this absolutely has nothing to do with frequency bandwidth.

[Kingston]

There actually IS a valid reason for using higher samplerates in summing (surprise there!), and it CAN make a significant difference depending on the summed signals.

I'll try a little diagram here to summarise the concept.

88.1khz signal:

|__._______|

another one:

|___.______|

both of those inaudible to anyone, and either of those at 44.1khz:

|_____| (nothing)

The two 88.1khz signals summed together:

|__..______|

The summed signal at 44.1khz:


|_.___|

huh? audible?

That's right. It CAN make a difference, but in realworld scenarios it's mostly insignificant impact on sound. It may or may not be audible, but the possibility is there, especially with something as complex as audio signals, and sharp transient content. (but only with mediocre samplerate conversion)



Food for thought that one, isn't?

[duncanparsons]

I'm considering ditching std UIs and going for ASCII art for VU meters...

Kingston - you've inspired me!

DSP

[Aleksey Vaneev]

Kingston, this concept is invalid. Frequencies up to Nyquist, and their phases can be represented *perfectly*. That means that summing at 192kHz and at 44.1kHz creates the same result. What you *may* hear is the difference caused by resampling. But I may suggest you to perform tests between 192kHz and 96kHz - they should exhibit identical summing results. Of course, 192kHz wave should be downsampled to 96kHz before comparison - and that's yet another step where difference can be introduced.

So, in practice its different (but in a neutral way), and in theory its identical.

[Kingston]

Kingston, this concept is invalid. Frequencies up to Nyquist, and their phases can be represented *perfectly*. That means that summing at 192kHz and at 44.1kHz creates the same result. What you *may* hear is the difference caused by resampling.

I didn't claim I can hear it, nor that there's any need to test it. It's simply an observation, and highly theoretical borderline case at that. It does work, but it is indeed samplerate conversion related problem if it bleeds back to audible range. In perfect world sinc would cancel the sums out.


I did make a mistake in my earlier post: of course it doesn't work in analog summing! [edited]

[Kingston]

I'm considering ditching std UIs and going for ASCII art for VU meters...DSP

You know, it might actually look really cool. Dead easy to code, too.

[voidar]

A 220500Hz sine-wave sampled at 44.1KHz is actually not a sine at all but a perfect square-wave, when represented digitally. Then through D/A's it is filtered (low-pass) to sound decent.

[Kingston]

A 22050Hz sine-wave sampled at 44.1KHz is actually not a sine at all but a perfect square-wave, when represented digitally. Then through D/A's it is filtered (low-pass) to sound decent.

Indeed. In ideal D/A the squarewave comes out as perfect sinewave, and the D/A quality of today is approaching the practical limits. The same thing applies to ALL audio signal processing: the squarewave is treated as a sinewave (generating a lot of practical computational problems at the same time).

[camsr]

Okay, now look at the situation like this...

lets say we have the frequency 22049hz, at 44100hz samplerate, and with 0 phase. do you know what's going to happen when they reach HALF of the LCM of 22049 and 44100? Complete silence. The peaks of the 22049hz signal will fall inbetween the sampling interval. So how does increasing the sampling rate help? at 192000hz, the signal-to-sampling ratio has a much greater LCM, and will catch the peaks of the signal far more often, resulting in a truer signal, that requires no interpolation to "fill in the blanks". Frequencies that do not divide the sample rate to a whole interger number will always have this problem. And at 44100hz, unless you have a really nice D/A, it's noticeable.

[Kingston]

Okay, now look at the situation like this...

lets say we have the frequency 22049hz, at 44100hz samplerate, and with 0 phase. do you know what's going to happen when they reach HALF of the LCM of 22049 and 44100? Complete silence. The peaks of the 22049hz signal will fall inbetween the sampling interval. So how does increasing the sampling rate help? at 192000hz, the signal-to-sampling ratio has a much greater LCM, and will catch the peaks of the signal far more often, resulting in a truer signal, that requires no interpolation to "fill in the blanks". Frequencies that do not divide the sample rate to a whole interger number will always have this problem. And at 44100hz, unless you have a really nice D/A, it's noticeable.

No camsr, really, no. It just doesn't work like that, it REALLY REALLY DOES NOT! and for the SEVENTEETH TIME IN THIS THREAD!

Understand nyquist sampling theory and the provided discrete (digital) time summation of consequent (sinc) samples, and you're off the placebo land.

[egbert]

One thing that might be worth adding is that a digital recording system does not output digital data - the sound as represented in the digital system is NOT the output.

Take the 1KHz sin wav example at 44.1 KHz - if you believe that delaying this wav by 10 usec in one channel cannot be represented in a system which operates with sampling at 25 usec you are mistaken.

If you sampled two incoming 1KHz sin waves that were delayed 10 usec with respect to one another the late channel would be delayed about 1% of a wavelength and all its samples would be shifted in value also. So if channel one is at a zero crossing the delayed channel will be at something like +/-2% of its amplitude in the time aligned sample. When you reconstuct the audio data from the digital data the audio output will be a sine wave which passes through all those sampled points and it will be delayed (surprise) 10 usec wrt the other channel - just as it was on the input.

Consider a tougher case - arrival of a steep transient - eg George Bush nukes a nearby neighbourhood or something. An extremely steep pressure wave rises out of the noise floor and hits your microphone diaphragm so hard it melts. With its dying breath the mic sends a signal to your 16 bit ADC down is ze bunker and if you look at the sample stream it looks like this:

0, 18,000, 32,000, goodnight nurse.

I used to think that therefore you could only specify the time of the explosion shockwave's arrival at the resolution of the sampling rate. But in fact when you turn the above set of samples back into audio (as a treat for your friends in the bunker) what will happen is that the DAC will create a steep wavefront which does NOT start with 25 usec of zero amplitude followed by a discrete jump up to over half full scale amplitude. It will start rising somewhere around halfway between the first two sampled points and draw a smooth curve through those points that starts before the first non zero one. This is what all that oversampling of the DACs is about.

[sambean]

Interesting stuff..

On the subject of frequencies close to Nyquist, if you have a sine wave at 22049Hz sampled at 44100Hz The sampled signal's first image will be at 22051Hz. You would need a pretty steep D/A filter to remove this image.. If you're unable to remove the image, is the sampled signal and it's first image not equivalent to a 22050Hz sine ring-modded with a 1Hz sine? so you would in fact get a 'beating' effect similar to what camsr was suggesting..

Isn't that why the 44100 sampling rate ensures nyquist is above most peoples range of perception, so we needn't worry about such things (unless of course you're called 'Barney' and like chasing sticks)...

Cheers

Sam

[voidar]

As far as I know, this is why oversampling is used. And before that, lowpass-filtering (for cut-off at peak-samplerate). It's all about correcting stuff so things will sound decent.

"Stuff" and "things", you know ..

[Kingston]

Isn't that why the 44100 sampling rate ensures nyquist is above most peoples range of perception, so we needn't worry about such things (unless of course you're called 'Barney' and like chasing sticks)...

Exactly, The lowpass filter starts sloping well before 22049Hz, usually at around 20khz, but that changes wildly between manufacturers and their filter implementations. The 22049Hz won't actually be recorded, as the filter should be at something like -60dB to -90dB around there. (again, depending on manufacturer).

It is better to record at 48khz for this reason, since some people *might* be able to hear slightly above 20-22khz (only small kids really). 48khz lowpass filter slope is more relaxed and starts well above 22khz.